Apply a Picture Texture
It seems that your cutout model is already extruded. 

Select the outline of your cutout and mark seams for unwrap.

Select all the front faces and unwrap them (Project from View is best in this case). 
Load your sonic picture in uv window and adjust the resize the unwrap (if the picture is in box size like 400x400, 512x512, it's going to fit perfect)

After this, in 3d view, Press Ctrl+I to invert the selection and unwrap it too. In Uv Window, press w and select weld (This turns the other selected faces into 1 single dot) and place the result where ever you seem appropriate. 

Give material to your model and add the sonic texture sheet.